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关键词： 定积分   等式   证明  

摘要： 定积分的计算是高等数学教学中的重点内容，计算问题往往灵活多变，需要学生掌握一定的方法和技巧，因此一些重要结论在定积分计算中至关重要。文章结合教学实际，给出了四个重要结论的证明及应用实例。

关键词： 随机分数延迟微分方程   分数微积分   指数欧拉-丸山方法   强收敛  

摘要： 1引言近年来,分数阶延迟微分方程因其能够准确地描述反常次扩散现象、超反常扩散现象和多孔介质问题等在力学、物理、电气工程、控制理论等学科中的应用较为广泛.因此,研究者们针对该方程做了大量的研究且取得了丰富的研究成果,比如:2011年,Bhalekar和Daftardargejji[1]扩展了Adams-Bashforth-Moulton算法来求解分数阶延迟微分方程;同年,杨水平[2]利用Jacobi谱配置方法数值求解了一类分数阶多项延迟微分方程,

关键词： 常微分方程   变量替换   求解  

摘要： 本文以一阶、二阶常微分方程为载体，对求解中变量替换的应用进行了分析、归纳，从而将常微分方程求解中的变量替换方法进行了拓展。

关键词： differential privacy   pseudo posterior distribution   pseudo posterior mecha-nism   synthetic data  

摘要： We propose a Bayesian pseudo posterior mechanism to generate record-level synthetic databases equipped with an (epsilon, pi) - probabilistic differential privacy (pDP) guarantee, where 7r denotes the probability that any observed database exceeds epsilon. The pseudo pos-terior mechanism employs a data record-indexed, risk-based weight vector with weight values is an element of [0, 1] that surgically downweight the likelihood contributions for high-risk records for model estimation and the generation of record-level synthetic data for public release. The pseudo posterior synthesizer constructs a weight for each datum record by using the Lipschitz bound for that record under a log-pseudo likelihood utility function that general-izes the exponential mechanism (EM) used to construct a formally private data generating mechanism. By selecting weights to remove likelihood contributions with non-finite log-likelihood values, we guarantee a finite local privacy guarantee for our pseudo posterior mechanism at every sample size. Our results may be applied to any synthesizing model envisioned by the data disseminator in a computationally tractable way that only involves estimation of a pseudo posterior distribution for parameters, theta, unlike recent approaches that use naturally-bounded utility functions implemented through the EM. We specify con-ditions that guarantee the asymptotic contraction of pi to 0 over the space of databases, such that the form of the guarantee provided by our method is asymptotic. We illustrate our pseudo posterior mechanism on the sensitive family income variable from the Consumer Expenditure Surveys database published by the U.S. Bureau of Labor Statistics. We show that utility is better preserved in the synthetic data for our pseudo posterior mechanism as compared to the EM, both estimated using the same non-private synthesizer, due to our use of targeted downweighting.

关键词： Multi-stage   magnetic gear   gear ratio   finite element analysis   torque ripple  

摘要： Magnetic gear is a non-contact transmission mechanism, which overcomes the drawback of mechanical gear transmission. Although the series multi-stage magnetic gear can provide a large gear ratio compared to the single-stage magnetic gear, the lower torque density of the series multi-stage magnetic gear limits its use in high-power wind turbines. According to the magnetic gear field modulation mechanism and the differential transmission method, a differential multi-stage coaxial magnetic gear transmission device is proposed, which can achieve transmission with a large gear ratio and large torque density. Based on the differential multi-stage coaxial magnetic gear structure and its working principle, the finite element method is used to simulate the electromagnetic performance of the multi-stage coaxial magnetic gear. Futhermore, the electromagnetic performance of the two stages of the proposed magnetic gear are compared. The results show that there is a significant difference between the the electromagnetic performance of the first stage and that of the second stage. The torque ripple of the first stage is more dramatic than that of the second stage. The torque ripple amplietude of the inner rotor of the first stage is 5.08 parts per thousand larger than that of the second stage. The torque ripple amplietude of the outer rotor of the first stage is 4.591 parts per thousand larger than that of the second stage.

关键词： 预制混凝土箱梁   畸变效应   能量变分法   微分方程  

摘要： 在预制混凝土箱梁设计分析时，结构畸变效应对桥梁变形的影响不可忽视。基于能量变分法，在建立预制混凝土箱梁的畸变效应微分方程的同时，给出计算预制混凝土箱梁的畸变双力矩和畸变角的理论公式，计算分析了箱梁横截面的高度、倾角和顶板宽度等参数对结构畸变效应的影响。结果表明：在跨中处，箱梁的畸变角和畸变双力矩均为最大值，二者沿梁长方向逐渐减小，直至趋近于零；箱梁的畸变双力矩和畸变角随截面高度的增大均有减小，但二者的变化程度不同；随着截面倾角和顶板宽度的增大，箱梁的畸变角和双力矩均有增加，变化程度不明显。

关键词： PBL教学模式   数学学科核心素养   一轮复习课  

摘要： 本文遵循“教师为主导、学生为中心、探究为主线”的教育理念，以落实高中数学学科核心素养为导向，在高三一轮复习课中实施PBL教学模式，注重学生的学习体验、推动合作学习、共同探究学习等学习方式的开展，使得学生成为学习的真正主体.

关键词： 三角函数   导数   性质  

摘要： 三角函数是初等函数之一，具有很多特殊性质，例如周期性、奇偶性、有界性等，在求导类大题中涉及到的三角函数，经常遇到求函数零点的问题，此时可以利用三角函数的特殊值去求其导函数的零点，来找到函数的极大值或极小值，三角函数的求导也很特殊，等同于图像向左移动π/2个单位，并不改变其周期性和有界性等性质，通过三角函数这些特殊性质，以及利用重要极限来合理放缩，可以解决大部分求导类大题中的三角函数问题.通过分析归纳此类问题，可以更好的培养学生数学抽象、逻辑推理及数学运算等核心素养.